A prismatic bar 𝑷𝑸𝑹𝑺𝑻 is subjected to axial loads as shown in the figure. The segments having maximum and minimum axial stresses, respectively, are

The correct option is QR and RS.

To determine the segments with the maximum and minimum axial stresses, we calculate the internal axial force in each segment of the prismatic bar. Let the constant cross-sectional area of the prismatic bar be $A$. The axial stress ($\sigma$) in any segment is directly proportional to the internal axial force ($F$) acting on that segment:

$$\sigma =\frac{F}{A}$$

Step 1: Calculate the support reaction at point P
Let $R_P$ be the horizontal reaction force at the fixed support $P$ acting to the left. Applying the equilibrium condition for the entire bar:

$$\sum F_x=0$$

From the given loading diagram, the forces pointing to the right are at $R$ ($15 \mathrm{kN}$) and $T$ ($25 \mathrm{kN}$). The forces pointing to the left are at $Q$ ($10 \mathrm{kN}$) and $S$ ($20 \mathrm{kN}$).
Equating the forces:

$$R_P+10 \mathrm{kN}+20 \mathrm{kN}=15 \mathrm{kN}+25 \mathrm{kN}$$

$$R_P+30 \mathrm{kN}=40 \mathrm{kN}$$

$$R_P=10 \mathrm{kN}\text{ (directed to the left)}$$

Step 2: Determine internal forces in each segment
Using the method of sections, we find the internal force in each segment:
- Segment PQ: Considering a section within segment $\mathrm{PQ}$ and looking to the left of the section:

$$F_{\mathrm{PQ}}=R_P=10 \mathrm{kN}\text{ (tension)}$$

- Segment QR: Considering a section within segment $\mathrm{QR}$ and looking to the left of the section:

$$F_{\mathrm{QR}}=R_P+10 \mathrm{kN}=10 \mathrm{kN}+10 \mathrm{kN}=20 \mathrm{kN}\text{ (tension)}$$

- Segment RS: Considering a section within segment $\mathrm{RS}$ and looking to the left of the section:

$$F_{\mathrm{RS}}=R_P+10 \mathrm{kN}-15 \mathrm{kN}=10 \mathrm{kN}+10 \mathrm{kN}-15 \mathrm{kN}=5 \mathrm{kN}\text{ (tension)}$$

Step 3: Compare stresses in the segments
Comparing the axial forces in the segments $\mathrm{PQ}$, $\mathrm{QR}$, and $\mathrm{RS}$:
- The maximum internal axial force occurs in segment QR with $F_{\max }=20 \mathrm{kN}$, which gives the maximum axial stress:

$${\sigma }_{\max }=\frac{20 \mathrm{kN}}{A}$$

- The minimum internal axial force occurs in segment RS with $F_{\min }=5 \mathrm{kN}$, which gives the minimum axial stress:

$${\sigma }_{\min }=\frac{5 \mathrm{kN}}{A}$$

Consequently, the segments experiencing the maximum and minimum axial stresses are QR and RS, respectively.